What is a Russian style in mathematics?

[Demystifier]

Many times I have seen the claim that some text on mathematics is written in a "good Russian style". What does that mean?

Somehow I've got an impression that it is a kind of opposite to the Bourbaki style. Namely, a Russian style would not consist of a dry series of abstract general theorems and proofs. Instead, it would contain a lot of practical examples that teach you how to apply math to practical problems. Is that correct? Or perhaps it means something else?

 

[S.G. Janssens]

Yes, I think to a considerable degree you are right. In my experience, the level of rigor may vary. I have read work by Russian mathematicians that is very applied and mathematically precise at the same time, see e.g. Mark Krasnosel'skii.

Perhaps you find some of the links on V.I. Arnold's wiki interesting. He had quite a strong opinion about mathematics' tendency towards increased abstraction. (Look for the phrase "Bourbaki" on that page.) You may find this biography useful as well. Of course, Russian style is not identically equal to Arnold's style, but he may provide a prominent example.

Incidentally, I find it difficult to really appreciate Arnold, for he has worked in so many fields (ranging from pure to applied) and I'm familiar with only a few of those. His books on differential equations and mechanics are not among my personal favorites.